Also took the time to test BV + SS vs a Swain who cast Nevermore.
I had BV, he cast Nevermore and I used SS. BV got hit first. I wasn't stared and SS ran out a moment later. Unfortunately, that's not the best synergy.
There's also a chance, that the effect that's cast first takes priority, so maybe it's the opposite if you use SS and BV recharger right after and you get hit right at that moment... but that's a very unlikely scenario, so I won't bother testing it.